3. You have the following information about two stocks: Expected return Standard

Question

3. You have the following information about two stocks: Expected return Standard deviation Beta Beyonce, Inc. 14.1% 9% 1.3 Jay Z, Ltd. 9.2% 7% 0.6 Assume you invest 70% of your funds in Beyonce and 30% in Jay Z, and the correlation of returns between the two is 0.4. Calculate the expected return, standard deviation, and beta of this portfolio. · . Calculate what happens to the expected return, standard deviation, and beta of the portfolio if the correlation of returns between the stocks is a) 1.0, b) 0.0, and c)-1.0.

Explanation / Answer

The expected return of the portfolio is given as= E(R) = w1R1 + w2Rq= 0.7*14.1 + 0.3*9.2 = 9.87+2.76 = 12.63%

We calculate portfolio variance in a simple two-asset portfolio as:

(weight(1)^2*variance(1) + weight(2)^2*variance(2) + 2*weight(1)*weight(2)*covariance(1,2)

Variance of the portfolio= (0.7^2)*(0.09^2) + (0.3^2)*(0.07^2) + 2*0.7*0.3*(0.4*0.09*0.07) = 0.005468

So, standard deviation of the portfolio= Sqrt(0.005468) = 0.074

Beta of the portfolio is given by the weighted sum of the individual asset betas.

So, beta of the portfolio= 0.7*1.3 + 0.3*0.6 = 0.91+0.18 = 1.09

Now let us consider the cases where the correlation of returns are different. The expected return and beta of the portfolio don't depend on correlation as shown in the formulas above. So they would remain the same as before. Let us calculate the new standard deviations of the portfolios:

a. correlation= 1.0

Variance of the portfolio= (0.7^2)*(0.09^2) + (0.3^2)*(0.07^2) + 2*0.7*0.3*(0.4*0.09*0.07) = 0.005468

So, standard deviation of the portfolio= Sqrt(0.005468) = 0.074

a. correlation= 1.0

Variance of the portfolio= (0.7^2)*(0.09^2) + (0.3^2)*(0.07^2) + 2*0.7*0.3*(1.0*0.09*0.07) = 0.007056

So, standard deviation of the portfolio= Sqrt(0.007056) = 0.084

b. correlation= 0.0

Variance of the portfolio= (0.7^2)*(0.09^2) + (0.3^2)*(0.07^2) + 2*0.7*0.3*(0.0*0.09*0.07) = 0.00441

So, standard deviation of the portfolio= Sqrt(0.00441) = 0.066

c. correlation= -1.0

Variance of the portfolio= (0.7^2)*(0.09^2) + (0.3^2)*(0.07^2) + 2*0.7*0.3*((-1)*0.09*0.07) = 0.001764

So, standard deviation of the portfolio= Sqrt(0.001764) = 0.042

Please revert to me in case of any queries :)

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